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Theory and design of optimum FIR compaction filters

Kiraç, Ahmet and Vaidyanathan, P. P. (1998) Theory and design of optimum FIR compaction filters. IEEE Transactions on Signal Processing, 46 (4). pp. 903-919. ISSN 1053-587X. http://resolver.caltech.edu/CaltechAUTHORS:KIRieeetsp98

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Abstract

The problem of optimum FIR energy compaction filter design for a given number of channels M and a filter order N is considered. The special cases where N<M and N=∞ have analytical solutions that involve eigenvector decomposition of the autocorrelation matrix and the power spectrum matrix, respectively. We deal with the more difficult case of M<N<∞. For the two-channel case and for a restricted but important class of random processes, we give an analytical solution for the compaction filter that is characterized by its zeros on the unit circle. This also corresponds to the optimal two-channel FIR filter bank that maximizes the coding gain under the traditional quantization noise assumptions. With a minor extension, this can also be used to generate optimal wavelets. For the arbitrary M-channel case, we provide a very efficient suboptimal design method called the window method. The method involves two stages that are associated with the above two special cases. As the order increases, the suboptimality becomes negligible, and the filter converges to the ideal optimal solution. We compare the window method with a previously introduced technique based on linear programming.


Item Type:Article
Additional Information:© Copyright 1998 IEEE. Reprinted with permission. Manuscript received February 15, 1997; revised November 30, 1997. This work was supported in part by the Office of Naval Research under Grant N00014-93-1-0231 and Tektronix, Inc. The associate editor coordinating the review of this paper and approving it for publication was Prof. Mark J. T. Smith.
Subject Keywords:Energy compaction, Nyquist filters, orthonormal filter banks, subband coding, wavelets
Record Number:CaltechAUTHORS:KIRieeetsp98
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:KIRieeetsp98
Alternative URL:http://dx.doi.org/10.1109/78.668545
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6286
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:30 Nov 2006
Last Modified:26 Dec 2012 09:19

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